Package preference. May 8, 2018

Transcription

1 Type Package Package preference May 8, 2018 Title 2-Stage Preference Trial Design and Analysis Version URL BugReports Design and analyze two-stage randomized trials with a continuous outcome measure. The package contains functions to compute the required sample size needed to detect a given preference, treatment, and selection effect; alternatively, the package contains functions that can report the study power given a fixed sample size. Finally, analysis functions are provided to test each effect using either summary data (i.e. means, variances) or raw study data. License LGPL-2 Imports ggplot2, tidyr Suggests testthat RoxygenNote LazyData true NeedsCompilation no Author Briana Cameron [aut, cph], Denise Esserman [ctb], Michael Kane [cre, ctb] Maintainer Michael Kane <michael.kane@yale.edu> Repository CRAN Date/Publication :05:32 UTC R topics documented: preference-package effects_from_means fit_preference

2 2 preference-package fit_preference_summary imap_stratified_summary optimal_proportion overall_power overall_sample_size preference preference.trial pt_from_power pt_from_ss pt_plot sample_size treatment_effect_size Index 20 preference-package Design and Analysis of Two-stage Randomized Clinical Trials The preference package is used for the design and analysis of two-stage randomized trials with a continuous outcome measure. In this study, patients are first randomized to either a random or choice arm. Patients initially randomized to the choice arm are allowed to select their preferred treatment from the available treatment options; patients initially randomized to the random arm undergo a second randomization procedure to one of the available treatment options. The design has also been extended to include important stratification variables; the functions provided in this package can accommodate both the unstratified and stratified designs. In this study, there are three effects that may be of interest. The treatment effect captures the difference in outcome between patients randomized to treatment A and treatment B (similar to a traditional RCT). The selection effect captures the difference in outcome between patients that prefer treatment A and patients that prefer treatment B, regardless of the treatment that is actually received. Finally, the preference effect compares the outcomes of patients who receive their preferred treatment (either treatment A or treatment B) and patients who do not receive their preferred treatment. To aid in the design of these two-stage randomized studies, sample size functions are provided to determine the necessary sample size to detect a particular selection, preference, and/or treatment effect. If the sample size is fixed prior to the start of the study, functions are provided to calculate the study power to detect each effect. Finally, the optimal_proportion function can be used to determine the optimal proportion of patients randomized to the choice arm in the initial randomization. To analyze the data from the two-stage randomized trial, two analysis functions are provided. The function analyze_raw_data computes the test statistic and p-value for each effect given provided raw study data. The function analyze_summary_data uses provided summary data (mean, variance, and sample size) of each study group to compute the test statistic and p-value of each effect. Sample Size Function calls selection_sample_size: required sample size to detect a given selection effect

3 preference-package 3 preference_sample_size: required sample size to detect a given preference effect treatment_sample_size: required sample size to detect a given treatment effect overall_sample_size: required sample size to detect a given set of selection, preference, and treatment effects Power Function Calls selection_power: study power to detect a given selection effect preference_power: study power to detect a given preference effect treatment_power: study power to detect a given treatment effect overall_power: study power to detect a given set of selection, preference, and treatment effects Analysis Function Calls analyze_raw_data: computes test statistic and p-value for observed selection, preference, and treatment effects using provided raw data analyze_summary_data: computes test statistic and p-value for observed selection, preference, and treatment effects using provided summary data (mean, variance, sample size) Other Function Calls treatment_effect_size: computes the treatment effect that can be detected given a specified sample size and power optimal_proportion: computes the optimal proportion randomized to choice arm (defined for unstratified design only) effects_from_means: computes the treatment, selection, and preference effect sizes provided the study means in each treatment arm Data Sets imap: summary SF36 outcome data for the two-stage randomized IMAP study imap_strat: summary SF36 outcome data for the two-stage randomized IMAP study stratified by high vs. low STAI score Acknowledgments: This work was partially supported through a Patient-Centered Outcomes Research Institute (PCORI) Award (ME ) and Yale s CTSA Award (Ul1TR001863). We would also like to thank the IMAP team for sharing their data to demonstrate this package. Disclaimer: All statements in this report, including its findings and conclusions, are solely those of the authors and do not necessarily represent the views of the Patient-Centered Outcomes Research Institute (PCORI), its Board of Governors or Methodology Committee. References Rucker G (1989). "A two-stage trial design for testing treatment, self-selection and treatment preference effects." Stat Med, 8(4): (PubMed) McCaffery et al. (2010) "Psychosocial outcomes of three triage methods for the management of borderline abnormal cervical smears: an open randomised trial." BMJ, 340:b4491. (PubMed)

4 4 effects_from_means Walter et. al. (2011). "Optimal allocation of participants for the estimation of selection, preference and treatment effects in the two-stage randomised trial design." Stat Med, 31(13): (PubMed) McCaffery et al. (2011) "Determining the Impact of Informed Choice: Separating Treatment Effects from the Effects of Choice and Selection in Randomized Trials." Med Decis Making, 31(2): (PubMed) Turner RM, et al. (2014). "Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects." Medical Decision Making, 34: (PubMed) Cameron B, Esserman D (2016). "Sample Size and Power for a Stratified Doubly Randomized Preference Design." Stat Methods Med Res. (PubMed) effects_from_means Calculate Effect Sizes from Means Calculates the preference, selection and treatment effects given the means of each treatment group in the choice and random arms for the 2-stage randomized study. effects_from_means(mu1, mu2, mu11, mu22, phi, nstrata = 1, xi = NULL) mu1 mu2 mean response of the patients receiving treatment 1 in the random arm. For unstratified design, should be numeric value. For the stratified design, should be vector of length equal to number of strata with each entry corresponding to stratum- specific mean. mean response of the patients receiving treatment 2 in the random arm. For unstratified design, should be numeric value. For the stratified design, should be vector of length equal to number of strata with each entry corresponding to stratum- specific mean. mu11 mean response of the patients choosing treatment 1 in the choice arm. For unstratified design, should be numeric value. For the stratified design, should be vector of length equal to number of strata with each entry corresponding to stratum- specific mean. mu22 mean response of the patients choosing treatment 2 in the choice arm. For unstratified design, should be numeric value. For the stratified design, should be vector of length equal to number of strata with each entry corresponding to stratum- specific mean. phi proportion of patients preferring treatment 1. For unstratified design, should be numeric value. For the stratified design, should be vector of length equal to number of strata with each entry corresponding to stratum-specific preference rate. All elements should be numeric values between 0 and 1.

5 fit_preference 5 nstrata xi number of strata. Default is 1 (unstratified design). a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. Should only be specified for stratified design. References Rucker G (1989). "A two-stage trial design for testing treatment, self-selection and treatment preference effects." Stat Med, 8(4): (PubMed) effects_from_means(mu1=1, mu2=2, mu11=1.5, mu22=2.5, phi=0.5) fit_preference Fit the Preference Data Collected from a Two-stage Clinical Trial Computes the test statistics and p-values for the preference, selection, and treatment effects for the two-stage randomized trial using collected outcome, random, treatment, and strata values for specified significance level. fit_preference(outcome, random, treatment, strata, alpha = 0.05) outcome random treatment strata alpha (numeric) individual trial outcomes. (logical) was this individual part of the random arm? (character, factor, or integer) which treatment an individual received (optional integer) which strata the individual belongs to. (optional numeric) Level of significance (default=0.05) # Unstratified outcome <- c(10, 8, 6, 10, 5, 8, 7, 6, 10, 12, 11, 6, 8, 10, 5, 7, 9, 12, 6, 8, 9, 10, 7, 8,11) random <- c(rep(false, 13), rep(true, 12)) treatment <- c(rep(1, 5), rep(2, 8), rep(1, 6), rep(2, 6)) fit_preference(outcome, random, treatment) # Stratified # Same data plus strata information. strata <- c(1,1,2,2,2,1,1,1,1,2,2,2,2,1,1,1,2,2,2,1,1,1,2,2,2) fit_preference(outcome, random, treatment, strata, alpha=0.1)

6 6 fit_preference_summary fit_preference_summary Fit Preference Model from Summary Data Computes the test statistics and p-values for the preference, selection, and treatment effects in a two-stage randomized trial using summary data. fit_preference_summary(x1mean, x1var, m1, x2mean, x2var, m2, y1mean, y1var, n1, y2mean, y2var, n2, xi = 1, nstrata = 1, alpha = 0.05) x1mean x1var m1 x2mean x2var m2 y1mean y1var n1 y2mean y2var n2 xi mean of responses for patients choosing treatment 1. If study is stratified, should be vector with length equal to the number of strata. variance of responses for patients choosing treatment 1. If study is stratified, should be vector with length equal to the number of strata. number of patients choosing treatment 1. If study is stratified, should be vector with length equal to the number of strata. mean of responses for patients choosing treatment 2. If study is stratified, should be vector with length equal to the number of strata. variance of responses for patients choosing treatment 2. If study is stratified, should be vector with length equal to the number of strata. number of patients choosing treatment 2. If study is stratified, should be vector with length equal to the number of strata. mean of responses for patients randomized to treatment 1. If study is stratified, should be vector with length equal to the number of strata. variance of responses for patients randomized to treatment 1. If study is stratified, should be vector with length equal to the number of strata. number of patients randomized to treatment 1. If study is stratified, should be vector with length equal to the number of strata. mean of responses for patients randomized to treatment 2. If study is stratified, should be vector with length equal to the number of strata. variance of responses for patients randomized to treatment 2. If study is stratified, should be vector with length equal to the number of strata. number of patients randomized to treatment 2. If study is stratified, should be vector with length equal to the number of strata. a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design).

7 fit_preference_summary 7 nstrata alpha number of strata. Default is 1 (i.e. unstratified design). Type I error rate, used to determine confidence interval level for the effect estimates. Default is 0.05 (i.e. 95% confidence interval) References Rucker G (1989). "A two-stage trial design for testing treatment, self-selection and treatment preference effects." Stat Med, 8(4): (PubMed) Cameron B, Esserman D (2016). "Sample Size and Power for a Stratified Doubly Randomized Preference Design." Stat Methods Med Res. (PubMed) # Unstratified x1mean <- 5 x1var <- 1 m1 <- 15 x2mean <- 7 x2var <- 1.1 m2 <- 35 y1mean <- 6 y1var <- 1 n1 <- 25 y2mean <- 8 y2var <- 1.2 n2 <- 25 fit_preference_summary(x1mean, x2var, m1, x2mean, x2var, m2, y1mean, y1var, n1, y2mean, y2var, n2) # Stratified x1mean <- c(5, 3) x1var <- c(1, 1) m1 <- c(15, 30) x2mean <- c(7, 7) x2var <- c(1.1, 3.1) m2 <- c(35, 40) y1mean <- c(6, 4) y1var <- c(1, 2) n1 <- c(25, 35) y2mean <- c(8, 12) y2var <- c(1.2, 1) n2 <- c(25, 20) fit_preference_summary(x1mean, x2var, m1, x2mean, x2var, m2, y1mean, y1var, n1, y2mean, y2var, n2, alpha=0.1)

8 8 optimal_proportion imap_stratified_summary Data from the the IMAP study The Improving Management of Abnormal Pap Smears study used a two-stage randomized preference trial design to evaluate psychosocial outcomes in women found to have atypical cells in a Pap Smear. Two systems for managing the atypical cells were tested (repeated Pap smears or HCV triage) and a doubly randomized design was used to evaluate the role of patient preference. The data set provides mean, standard deviation and sample sizes of the SF36 outcome for each treatment in both the choice and random arms. Three data sets are provided with the preference package based on the IMAP study. The first, imap_summary provides summary statistics of the entire trial. The second imap_summary_stratified, summary statistics of the study per strata. The third imap is a resampled version of the individual level data including stratification. Each of these data sets are compatible with the analysis functions fit_preference_summary, fit_preference, and preference, provided in this package. The examples sections in the documentation illustrate their use. References McCaffery et al. (2010) "Psychosocial outcomes of three triage methods for the management of borderline abnormal cervical smears: an open randomised trial." BMJ, 340:b4491. (PubMed) McCaffery et al. (2011) "Determining the Impact of Informed Choice: Separating Treatment Effects from the Effects of Choice and Selection in Randomized Trials." Med Decis Making, 31(2): (PubMed) optimal_proportion Unstratified Optimized Theta Calculates the optimal proportion of patients assigned to the choice arm in an unstratified two-stage randomized trial optimal_proportion(w_sel, w_pref, w_treat, sigma2, phi, delta_pi, delta_nu)

9 overall_power 9 w_sel w_pref w_treat sigma2 phi delta_pi delta_nu weight assigned to the estimation of the selection effect. Each weight should be a numeric value between 0 and 1 and sum of three weights should be 1. weight assigned to the estimation of the preference effect. Each weight should be a numeric value between 0 and 1 and sum of three weights should be 1. weight assigned to estimation of the treatment effect. Each weight should be a numeric value between 0 and 1 and sum of three weights should be 1. variance estimate. Should be a positive numeric value. proportion of patients preferring treatment 1. Should be numeric value between 0 and 1. overall study preference effect. overall study selection effect. References Walter et. al. (2011). "Optimal allocation of participants for the estimation of selection, preference and treatment effects in the two-stage randomised trial design." Stat Med, 31(13): (PubMed) optimal_proportion(w_sel=0.2, w_pref=0.4, w_treat=0.4, sigma2=1, phi=0.5, delta_pi=1, delta_nu=0.5) overall_power Power Calculation from Sample Size Calculates the study power to detect a set of effects given a particular sample size in a two-stage randomized clinical trial overall_power(n, phi, sigma2, delta_pi, delta_nu, delta_tau, alpha = 0.05, theta = 0.5, xi = 1, nstrata = 1, k = 1) N phi overall study sample size. the proportion of patients preferring treatment 1. Should be numeric value between 0 and 1. If study is stratified, should be vector with length equal to the number of strata in the study.

10 10 overall_sample_size sigma2 delta_pi delta_nu delta_tau alpha theta xi nstrata variance estimate. Should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. overall study preference effect. overall study selection effect. overall study treatment effect. desired type I error rate. proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5). a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design). number of strata. Default is 1 (i.e. unstratified design). k the ratio of treatment A to treatment B in the random arm (default 1). References Turner RM, et al. (2014). "Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects." Medical Decision Making, 34: (PubMed) Cameron B, Esserman D (2016). "Sample Size and Power for a Stratified Doubly Randomized Preference Design." Stat Methods Med Res. (PubMed) overall_sample_size Overall Sample Size Calculates the sample size required to detect a given set of effects in a two-stage randomized clinical trial. Returns the largest of the required sample sizes for a given set of treatment, selection, and preference effects. overall_sample_size(power, phi, sigma2, delta_pi, delta_nu, delta_tau, alpha = 0.05, theta = 0.5, xi = 1, nstrata = 1, k = 1) power desired study power. Should be numeric value between 0 and 1. phi the proportion of patients preferring treatment 1. Should be numeric value between 0 and 1. If study is stratified, should be vector with length equal to the number of strata in the study.

11 preference 11 sigma2 delta_pi delta_nu delta_tau alpha theta xi nstrata k variance estimate. Should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. overall study preference effect. overall study selection effect. overall study treatment effect. desired type I error rate. proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5). a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design). number of strata. Default is 1 (i.e. unstratified design). the ratio of treatment A to treatment B in the random arm. (default 1, i.e. equal distribution to the two treatments in the random arm) References Turner RM, et al. (2014). "Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects." Medical Decision Making, 34: (PubMed) Cameron B, Esserman D (2016). "Sample Size and Power for a Stratified Doubly Randomized Preference Design." Stat Methods Med Res. (PubMed) preference Fit Preference Data Collected from a Two-stage Clinical Trial The variables in the formula should reference columns in the data parameter and should have the following characteristics. outcome: Numeric values giving the outcome of interest. treatment: Character, categorical, or integer values denoting the treatment received by an individual. arm: Logical value indicating whether the sample was from the random arm (TRUE) or choice (FALSE). strata: An optional integer value denoting which strata individuals belong to. preference(form, data, alpha = 0.05)

12 12 preference.trial form data a formula of the form outcome ~ treatment:arm { strata}. See Details for more explanation. a data.frame containing variables specified in the formula alpha (optional numeric) Level of significance (default 0.05) # Unstratified outcome <- c(10, 8, 6, 10, 5, 8, 7, 6, 10, 12, 11, 6, 8, 10, 5, 7, 9, 12, 6, 8, 9, 10, 7, 8, 11) arm <- c(rep("choice", 13), rep("random", 12)) treatment <- c(rep(1, 5), rep(2, 8), rep(1, 6), rep(2, 6)) d <- data.frame(outcome=outcome, treatment=treatment, arm=arm) preference(outcome ~ treatment:arm, d) # Stratified outcome <- c(10, 8, 6, 10, 5, 8, 7, 6, 10, 12, 11, 6, 8, 10, 5, 7, 9, 12, 6, 8, 9, 10, 7, 8,11) random <- c(rep(false, 13), rep(true, 12)) treatment <- c(rep(1, 5), rep(2, 8), rep(1, 6), rep(2, 6)) strata <- c(1,1,2,2,2,1,1,1,1,2,2,2,2,1,1,1,2,2,2,1,1,1,2,2,2) d <- data.frame(outcome=outcome, treatment=treatment, arm=arm, strata=strata) preference(outcome ~ treatment:arm strata, d, alpha=0.1) preference.trial Create a Preference Trial Create a Preference Trial preference.trial(pref_ss, pref_effect, selection_ss, selection_effect, treatment_ss, treatment_effect, sigma2, pref_prop, choice_prop = 0.5, stratum_prop = 1, alpha = 0.05, k = 1) pref_ss pref_effect selection_ss the sample size of the preference arm. the effect size of the preference arm (delta_pi). the sample size of the selection arm.

13 preference.trial 13 selection_effect the effect size of selection arm (delta_nu). treatment_ss the sample size of the treatment arm. treatment_effect the sample size of the treatment arm (delta_tau) sigma2 pref_prop choice_prop stratum_prop the variance estimate of the outcome of interest. This value should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. the proportion of patients preferring treatment 1. This value should be between 0 and 1 (phi). the proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5) (theta). xi a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design) (xi). alpha the desired type I error rate (default 0.05). k the ratio of treatment A to treatment B in the random arm (default 1).. References Turner RM, et al. (2014). "Sample Size and Power When Designing a Randomized Trial for the Estimation of Treatment, Selection, and Preference Effects." Medical Decision Making, 34: (PubMed) Cameron B, Esserman D (2016). "Sample Size and Power for a Stratified Doubly Randomized Preference Design." Stat Methods Med Res. (PubMed) # Unstratified single trial. preference.trial(pref_ss=100, pref_effect=1, selection_ss=100, selection_effect=1, treatment_ss=100, treatment_effect=1, sigma2=1, pref_prop=0.6) # Stratified single trial. preference.trial(pref_ss=100, pref_effect=1, selection_ss=100, selection_effect=1, treatment_ss=100, treatment_effect=1, sigma2=list(c(1, 0.8)), pref_prop=list(c(0.6, 0.3)), choice_prop=0.5, stratum_prop=list(c(0.3, 0.7))) # Multiple trials unstratified. preference.trial(pref_ss=100, pref_effect=seq(0.1, 2, by=0.5), selection_ss=100, selection_effect=1, treatment_ss=100, treatment_effect=1, sigma2=1, pref_prop=0.6) # Multiple, stratified trials. preference.trial(pref_ss=100, pref_effect=seq(0.1, 2, by=0.5),

14 14 pt_from_power selection_ss=100, selection_effect=1, treatment_ss=100, treatment_effect=1, sigma2=list(c(1, 0.8)), pref_prop=list(c(0.6, 0.3)), choice_prop=0.5, stratum_prop=list(c(0.3, 0.7))) pt_from_power Design Preference Trials with Power Constraint(s) Create a set of preference trials with specified power. The power parameter guarantees that the power will be at least what is specified for each of the three arms. pt_from_power(power, pref_effect, selection_effect, treatment_effect, sigma2, pref_prop, choice_prop = 0.5, stratum_prop = 1, alpha = 0.05, k = 1) power pref_effect the desired power(s) for the trial(s) the effect size of the preference arm (delta_pi). selection_effect the effect size of selection arm (delta_nu). treatment_effect the sample size of the treatment arm (delta_tau) sigma2 pref_prop choice_prop stratum_prop the variance estimate of the outcome of interest. This value should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. the proportion of patients preferring treatment 1. This value should be between 0 and 1 (phi). the proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5) (theta). xi a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design) (xi). alpha the desired type I error rate (default 0.05). k the ratio of treatment A to treatment B in the random arm (default 1)..

15 pt_from_ss 15 # Unstratified trials with power constraints. pt_from_power(power=seq(.1, 0.8, by=0.1), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=1, pref_prop=0.6) # Stratified trials with power constraints. Note that the proportion # of patients in the choice arm (choice prop) is fixed for all strata. pt_from_power(power=seq(0.1, 0.8, by=0.1), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=list(c(1, 0.8)), pref_prop=list(c(0.6, 0.3)), choice_prop=0.5, stratum_prop=list(c(0.3, 0.7))) # or... pt_from_power(power=seq(0.1, 0.8, by=0.1), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=c(1, 0.8), pref_prop=c(0.6, 0.3), choice_prop=0.5, stratum_prop=c(0.3, 0.7)) pt_from_ss Design Preference Trials with Sample Size Constraint(s) Create a set of preference trials where the maximum sample size for an arm is specified. pt_from_ss(ss, pref_effect, selection_effect, treatment_effect, sigma2, pref_prop, choice_prop = 0.5, stratum_prop = 1, alpha = 0.05, k = 1) ss the maximum size of any of the three arms. pref_effect the effect size of the preference arm (delta_pi). selection_effect the effect size of selection arm (delta_nu). treatment_effect the sample size of the treatment arm (delta_tau) sigma2 pref_prop the variance estimate of the outcome of interest. This value should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. the proportion of patients preferring treatment 1. This value should be between 0 and 1 (phi).

16 16 pt_plot choice_prop stratum_prop the proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5) (theta). xi a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design) (xi). alpha the desired type I error rate (default 0.05).. k the ratio of treatment A to treatment B in the random arm (default 1). # Unstratified trials with power constraints. pt_from_ss(ss=seq(100, 1000, by=100), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=1, pref_prop=0.6) # Stratified trials with power constraints. Note that the proportion # of patients in the choice arm (choice prop) is fixed for all strata. pt_from_ss(ss=seq(100, 1000, by=100), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=list(c(1, 0.8)), pref_prop=list(c(0.6, 0.3)), choice_prop=0.5, stratum_prop=list(c(0.3, 0.7))) # or... pt_from_ss(ss=seq(100, 1000, by=100), pref_effect=1, selection_effect=1, treatment_effect=1, sigma2=c(1, 0.8), pref_prop=c(0.6, 0.3), choice_prop=0.5, stratum_prop=c(0.3, 0.7)) pt_plot Plot the effect sizes of a preference trial The pt_plot() function visualizes the change in the preference effect, the selection effect, or both as a function of the total sample size of the trial. If the preference effect varies but the selection effect does not, then it plots the preference effect by the total sample size. Similarly if the selection effect varies but not the preference effect then selection effect vs total sample size is shown. When both preference and selection effect vary then the selection effect is shown conditioned on the given preference effects. It is assumed that the set of trial provided as a parameter are related and are comparable. For example, the function does not check to if the strata are the same for all trials. If some other visualization is required then the user is reminded that a preference.trial object is a data frame and can be visualized in the usual way.

17 sample_size 17 pt_plot(pt) pt an object of class preference.trial. # Plot trials with fixed power and varying preference effect. trials <- pt_from_power(power = 0.8, pref_effect = seq(0.5, 2, by = 0.1), selection_effect = 1, treatment_effect = 1, sigma2 = 1, pref_prop = 0.6) pt_plot(trials) # Plot trials with fixed power and varying selection effect. trials <- pt_from_power(power = 0.8, pref_effect = 1, selection_effect = seq(0.5, 2, by = 0.1), treatment_effect = 1, sigma2 = 1, pref_prop = 0.6) pt_plot(trials) # Plot trials with fixed power and varying preference and # selection effects. # the selection effects of interest selection_effects <- rep(seq(0.5, 2, by = 0.1), 4) # the preference effects to condition on pref_effects <- rep(seq(0.4, 1, by = 0.2), each = length(selection_effects)/4) trials <- pt_from_power(power = 0.8, pref_effect = pref_effects, selection_effect = selection_effects, treatment_effect = 1, sigma2 = 1, pref_prop = 0.6) pt_plot(trials) sample_size Preference trial parameter accessors Accessor function have been created to get the sample size (sample_size), power (power), effect size (effect_size), arm proportion (proportion), significance (significance), and trial variance estimates (sigma2) for a set of preference trials. Note that these methods are preferred over accessing the underlying data frame directly since the structure is slightly non-standard (some columns are lists) and some values, like power, are not stored directly.

18 18 sample_size sample_size(x) ## S3 method for class 'preference.trial' sample_size(x) power(x) ## S3 method for class 'preference.trial' power(x) effect_size(x) ## S3 method for class 'preference.trial' effect_size(x) proportion(x) ## S3 method for class 'preference.trial' proportion(x) significance(x) ## S3 method for class 'preference.trial' significance(x) sigma2(x) ## S3 method for class 'preference.trial' sigma2(x) x the set of preference trials. # Create a set of trials with a sequence of preference effects. trials <- preference.trial(pref_ss=100, pref_effect=seq(0.1, 2, by=0.5), selection_ss=100, selection_effect=1, treatment_ss=100, treatment_effect=1, sigma2=1, pref_prop=0.6) # the sample sizes sample_size(trials) # the powers power(trials)

19 treatment_effect_size 19 # the effect sizes effect_size(trials) # the arm proportions proportion(trials) # the significance significance(trials) # the variance estimates sigma2(trials) treatment_effect_size Treatment Effect Back Calculation Calculates the treatment effect that can be detected given a desired study power and overall study sample size for the two-stage randomized design treatment_effect_size(n, power, sigma2, alpha = 0.05, theta = 0.5, xi = 1, nstrata = 1) N overall study sample size. power desired study power. Should be numeric value between 0 and 1. sigma2 alpha theta xi nstrata variance estimate. Should be positive numeric values. If study is stratified, should be vector of within-stratum variances with length equal to the number of strata in the study. desired type I error rate. proportion of patients assigned to choice arm in the initial randomization. Should be numeric value between 0 and 1 (default=0.5). a numeric vector of the proportion of patients in each stratum. Length of vector should equal the number of strata in the study and sum of vector should be 1. All vector elements should be numeric values between 0 and 1. Default is 1 (i.e. unstratified design). number of strata. Default is 1 (i.e. unstratified design). treatment_effect_size(n=300, power=0.9, sigma2=c(1,0.8), xi=c(0.3,0.7), nstrata=2)

20 Index Topic data imap_stratified_summary, 8 effect_size (sample_size), 17 effects_from_means, 4 fit_preference, 5 fit_preference_summary, 6 imap (imap_stratified_summary), 8 imap_stratified_summary, 8 imap_summary (imap_stratified_summary), 8 optimal_proportion, 8 overall_power, 9 overall_sample_size, 10 power (sample_size), 17 preference, 11 preference-package, 2 preference.trial, 12 proportion (sample_size), 17 pt_from_power, 14 pt_from_ss, 15 pt_plot, 16 sample_size, 17 sigma2 (sample_size), 17 significance (sample_size), 17 treatment_effect_size, 19 20